Re:In the digits of pi (Score 2)

Not necessarily. Even though PI isn't a rational number, it doesn't mean that it necessarily contains any given subsequence. Let me take another non-rational number: 0.12112111211112... It won't ever contain the prime number 3, nor will it contain the complete works of Shakespeare. PI is similarly constrained to a specific pattern. I agree that an infinite un-patterned sequence will contain such sequences, but whether you include or exclude the axiom of choice will determine whether such numbers exist or not. Whether or not PI actually contains all primes as subsequences, I don't know. I'd suggest you present a proof one way or the other.